What is the Greatest Common Factor of 30176 and 30192?

Greatest common factor (GCF) of 30176 and 30192 is 16.

GCF(30176,30192) = 16

We will now calculate the prime factors of 30176 and 30192, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30176 and 30192.

How to find the GCF of 30176 and 30192?

We will first find the prime factorization of 30176 and 30192. After we will calculate the factors of 30176 and 30192 and find the biggest common factor number .

Step-1: Prime Factorization of 30176

Prime factors of 30176 are 2, 23, 41. Prime factorization of 30176 in exponential form is:

30176 = 2⁵ × 23¹ × 41¹

Step-2: Prime Factorization of 30192

Prime factors of 30192 are 2, 3, 17, 37. Prime factorization of 30192 in exponential form is:

30192 = 2⁴ × 3¹ × 17¹ × 37¹

Step-3: Factors of 30176

List of positive integer factors of 30176 that divides 30176 without a remainder.

1, 2, 4, 8, 16, 23, 32, 41, 46, 82, 92, 164, 184, 328, 368, 656, 736, 943, 1312, 1886, 3772, 7544, 15088

Step-4: Factors of 30192

List of positive integer factors of 30192 that divides 30176 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 37, 48, 51, 68, 74, 102, 111, 136, 148, 204, 222, 272, 296, 408, 444, 592, 629, 816, 888, 1258, 1776, 1887, 2516, 3774, 5032, 7548, 10064, 15096

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30176 and 30192. The biggest common factor number is the GCF number.
So the greatest common factor 30176 and 30192 is 16.

Also check out the Least Common Multiple of 30176 and 30192